Amazon.com Inc. said it plans to start a new music streaming service that—like at least half a dozen competitors—offers on-demand, unlimited access to tens of millions of songs for a monthly fee.

Distinguishing Amazon Music Unlimited, which was to launch Wednesday: Customers using the retail giant’s voice-activated Echo speakers will pay just $3.99 a month—less than half the $9.99 charged by most rivals—and will be able to stream music in a markedly different way.